Theorems · Theorem · order theory
Set.Nontrivial.not_subsingleton
∀ {α : Type u} {s : Set α}, s.Nontrivial → ¬s.SubsingletonAlias of the reverse direction of Set.not_subsingleton_iff.
- Defined in
- Mathlib.Data.Set.Subsingleton
- Cited by
- 5 results in Mathlib
- Foundations
- Depth 15 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites4
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Setstatement and proof · cited by 53,352
- Set.Subsingletonstatement · cited by 276
- Set.Nontrivialstatement · cited by 145
- Set.not_subsingleton_iffproof · cited by 7
Cited by5
Results whose statement or proof uses this declaration.
- RelSeries.length_ne_zero_of_nontrivialproof · cited by 2
- SimpleGraph.edgeDisjointTriangles_iff_mem_sym2_subsingletonproof · cited by 1
- SimpleGraph.isClique_map_iffproof · cited by 1
- SimpleGraph.isClique_map_image_iffproof · cited by 0
- ValuativeRel.IsDiscrete.of_compatible_withZeroMulIntproof · cited by 0